Abstract. Path integration is a primary means of navigation for a number of animals. We present a model which performs path integration with a neural network. This model is based on a neural structure called a sinusoidal array, which allows an efficient representation of vector information with neurons. We show that exact path integration can easily be achieved by a neural network. Thus deviations from the direct home trajectory, found previously in experiments with ants, can not be explained by computational limitations of the nervous system. Instead we suggest that the observed deviations are caused by a strategy to simplify landmark navigation.

No abstract

Electrophysiological studies in various sensory systems of different species show that many neurons involved in object localization have large receptive fields. This seems to contradict the high sensory resolution and the behavioral precision observed in localization experiments. Assuming a coarse coding mechanism, the resolution obtained by an ensemble of neurons is analytically calculated as a function of receptive field size. It is shown that particularly large receptive fields yield a high resolution.

Feedback systems with a single delay time-as described by delay-differential equations

Using extracellular recordings and computational modeling, we study the responses of a population of turtle (Pseudemys scripta elegans) retinal ganglion cells to different motion patterns. The onset of motion of a bright bar is signaled by a rise of the population activity that occurs within less than 100 ms. Correspondingly, more complex stimulus movement patterns are reflected by rapid variations of the firing rate of the retinal ganglion cell population. This behavior is reproduced by a computational model that generates ganglion cell activity from the spatio-temporal stimulus pattern using a Wiener model complemented by a non-linear contrast gain control feedback loop responsible for the sharp transients in response to motion onset. This study demonstrates that contrast gain control strongly influences the temporal course of retinal population activity, and thereby plays a major role in the formation of a population code for stimulus movement patterns.